Question

Ted buys sand and shovels at the beach with his allowance money. His preferences for sand and shovels are homothetic. Ben gets $3 in allowance money and shovels costs $.50 per shovel. He chooses to get one unit of shovels. His parents would like him to get 2 units of shovels. How much extra allowance money do they need to give Ted in order for him to choose to get 2 shovels?

Answer 1

In this regard, if they are homothetic preferences, what happens is that the proportion of shovels and sand demanded would remain same with the income and increase proportionately with the increase in the income on the whole and because at $3 you are getting one unit of shovel and the rest of the money you are giving for sand, in order to get one extra unit of show will you have to increase the income by same proportion where for one unit of shovel you need $3 of allowance and this means for two units of shovel

Allowance required = 2 *$3 = $6

Therefore additional allowance required equal to $6-$3 = $3 is the answer to this question